A Martingale Result for Convexity Adjustment in the Black Pricing Model

Eric Benhamou ()

Finance from EconWPA

Abstract: This paper explains how to calculate convexity adjustment for interest rates derivatives when assuming a deterministic time dependent volatility, using martingale theory. The motivation of this paper lies in two directions. First, we set up a proper no-arbitrage framework illustrated by a relationship between yield rate drift and bond price. Second, making ap-proximation, we come to a closed formula with speci…cation of the error term. Earlier works (Brotherton et al. (1993) and Hull (1997)) assumed constant volatility and could not specify the approximation error. As an application, we examine the convexity bias between CMS and forward swap rates.

Keywords: Martingale; Convexity Adjustment; Black and Black Scholes volatility; CMS rates. (search for similar items in EconPapers)
JEL-codes: G13 G12 (search for similar items in EconPapers)
Date: 2002-12-21
Note: Type of Document - PDF; prepared on windows; pages: 118
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpfi:0212005

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